An extension of Billingsley’s uniform boundedness theorem to higher-dimensional M -processes

Jana Jurečková; Pranab Kumar Sen

Kybernetika (1987)

  • Volume: 23, Issue: 5, page 382-387
  • ISSN: 0023-5954

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Jurečková, Jana, and Sen, Pranab Kumar. "An extension of Billingsley’s uniform boundedness theorem to higher-dimensional $M$-processes." Kybernetika 23.5 (1987): 382-387. <http://eudml.org/doc/29035>.

@article{Jurečková1987,
author = {Jurečková, Jana, Sen, Pranab Kumar},
journal = {Kybernetika},
keywords = {robust estimation in general linear models; asymptotic linearity results; tightness; uniform boundedness in probability; multiparameter stochastic processes},
language = {eng},
number = {5},
pages = {382-387},
publisher = {Institute of Information Theory and Automation AS CR},
title = {An extension of Billingsley’s uniform boundedness theorem to higher-dimensional $M$-processes},
url = {http://eudml.org/doc/29035},
volume = {23},
year = {1987},
}

TY - JOUR
AU - Jurečková, Jana
AU - Sen, Pranab Kumar
TI - An extension of Billingsley’s uniform boundedness theorem to higher-dimensional $M$-processes
JO - Kybernetika
PY - 1987
PB - Institute of Information Theory and Automation AS CR
VL - 23
IS - 5
SP - 382
EP - 387
LA - eng
KW - robust estimation in general linear models; asymptotic linearity results; tightness; uniform boundedness in probability; multiparameter stochastic processes
UR - http://eudml.org/doc/29035
ER -

References

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  1. P. Bickel, M. J. Wichura, Convergence criteria for multiparameter stochastic processes and some applications, Ann. Math. Statist. 42 (1971), 1656-1670. (1971) Zbl0265.60011MR0383482
  2. P. Billingsley, Convergence of Probability Measures, J. Wiley, New York 1968. (1968) Zbl0172.21201MR0233396
  3. J. Jurečková, P. K. Sen, Invariance principles for some stochastic processes related to M-estimators and their role in sequential statistical inference, Sankhya, Ser. A 43 (1981), 190-210. (1981) MR0666380
  4. J. Jurečková, P. K. Sen, Sequential procedures based on M-estimators with discontinuous score functions, J. Statist. Plan Infer. 5 (1981), 253-266. (1981) MR0635900
  5. J. Jurečková, P. K. Sen, On adaptive scale-equivariant M-estimators in linear models, Statist. & Dec, Suppl. Issue No. 1 (1984), 31 - 46. (1984) MR0785200
  6. J. Jurečková, P. K. Sen, A second order asymptotic distributional representation of M-estimators with discontinuous score functions, Ann. Probab. 15 (1987), 814-823. (1987) MR0885146
  7. A. H. Welsh, Bahadur representations for robust scale estimators based on regression residuals, Ann. Statist. 14 (1986), 1246-1251. (1986) Zbl0604.62028MR0856820

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